Sr Examen
Otras calculadoras
- Derivada de una función implícitamente dada
- Derivada de una función paramétrica
- Derivada parcial de la función
- Análisis de la función gráfica
- Integrales paso a paso
- Ecuaciones diferenciales paso a paso
- Límites paso por paso
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¿Cómo usar?
- Derivada de:
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Derivada de (-4)/x^2
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Derivada de 2/x²
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Derivada de -2*y
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Derivada de (3+2x)/(x-5)
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Expresiones idénticas
- y=(ctg5x)^ln2x
- y es igual a (ctg5x) en el grado ln2x
- y=(ctg5x)ln2x
- y=ctg5xln2x
- y=ctg5x^ln2x
Derivada de y=(ctg5x)^ln2x
Solución
Ha introducido
[src]
log(2*x) cot (5*x)
$$\cot^{\log{\left(2 x \right)}}{\left(5 x \right)}$$
cot(5*x)^log(2*x)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
/ / 2 \ \
log(2*x) |log(cot(5*x)) \-5 - 5*cot (5*x)/*log(2*x)|
cot (5*x)*|------------- + ---------------------------|
\ x cot(5*x) /
$$\left(\frac{\left(- 5 \cot^{2}{\left(5 x \right)} - 5\right) \log{\left(2 x \right)}}{\cot{\left(5 x \right)}} + \frac{\log{\left(\cot{\left(5 x \right)} \right)}}{x}\right) \cot^{\log{\left(2 x \right)}}{\left(5 x \right)}$$
Segunda derivada
[src]
/ 2 2 \
|/ / 2 \ \ / 2 \ / 2 \|
log(2*x) || log(cot(5*x)) 5*\1 + cot (5*x)/*log(2*x)| log(cot(5*x)) / 2 \ 25*\1 + cot (5*x)/ *log(2*x) 10*\1 + cot (5*x)/|
cot (5*x)*||- ------------- + --------------------------| - ------------- + 50*\1 + cot (5*x)/*log(2*x) - ---------------------------- - ------------------|
|\ x cot(5*x) / 2 2 x*cot(5*x) |
\ x cot (5*x) /
$$\left(\left(\frac{5 \left(\cot^{2}{\left(5 x \right)} + 1\right) \log{\left(2 x \right)}}{\cot{\left(5 x \right)}} - \frac{\log{\left(\cot{\left(5 x \right)} \right)}}{x}\right)^{2} - \frac{25 \left(\cot^{2}{\left(5 x \right)} + 1\right)^{2} \log{\left(2 x \right)}}{\cot^{2}{\left(5 x \right)}} + 50 \left(\cot^{2}{\left(5 x \right)} + 1\right) \log{\left(2 x \right)} - \frac{10 \left(\cot^{2}{\left(5 x \right)} + 1\right)}{x \cot{\left(5 x \right)}} - \frac{\log{\left(\cot{\left(5 x \right)} \right)}}{x^{2}}\right) \cot^{\log{\left(2 x \right)}}{\left(5 x \right)}$$
Tercera derivada
[src]
/ 3 / 2 \ 3 2 2 \
| / / 2 \ \ / / 2 \ \ | / 2 \ / 2 \ | / 2 \ / 2 \ / 2 \ / 2 \ / 2 \ |
log(2*x) | | log(cot(5*x)) 5*\1 + cot (5*x)/*log(2*x)| 2*log(cot(5*x)) | log(cot(5*x)) 5*\1 + cot (5*x)/*log(2*x)| |log(cot(5*x)) / 2 \ 10*\1 + cot (5*x)/ 25*\1 + cot (5*x)/ *log(2*x)| 150*\1 + cot (5*x)/ / 2 \ 250*\1 + cot (5*x)/ *log(2*x) 75*\1 + cot (5*x)/ 15*\1 + cot (5*x)/ 500*\1 + cot (5*x)/ *log(2*x)|
cot (5*x)*|- |- ------------- + --------------------------| + --------------- + 3*|- ------------- + --------------------------|*|------------- - 50*\1 + cot (5*x)/*log(2*x) + ------------------ + ----------------------------| + ------------------- - 500*\1 + cot (5*x)/*cot(5*x)*log(2*x) - ----------------------------- - ------------------- + ------------------ + -----------------------------|
| \ x cot(5*x) / 3 \ x cot(5*x) / | 2 x*cot(5*x) 2 | x 3 2 2 cot(5*x) |
\ x \ x cot (5*x) / cot (5*x) x*cot (5*x) x *cot(5*x) /
$$\left(- \left(\frac{5 \left(\cot^{2}{\left(5 x \right)} + 1\right) \log{\left(2 x \right)}}{\cot{\left(5 x \right)}} - \frac{\log{\left(\cot{\left(5 x \right)} \right)}}{x}\right)^{3} + 3 \left(\frac{5 \left(\cot^{2}{\left(5 x \right)} + 1\right) \log{\left(2 x \right)}}{\cot{\left(5 x \right)}} - \frac{\log{\left(\cot{\left(5 x \right)} \right)}}{x}\right) \left(\frac{25 \left(\cot^{2}{\left(5 x \right)} + 1\right)^{2} \log{\left(2 x \right)}}{\cot^{2}{\left(5 x \right)}} - 50 \left(\cot^{2}{\left(5 x \right)} + 1\right) \log{\left(2 x \right)} + \frac{10 \left(\cot^{2}{\left(5 x \right)} + 1\right)}{x \cot{\left(5 x \right)}} + \frac{\log{\left(\cot{\left(5 x \right)} \right)}}{x^{2}}\right) - \frac{250 \left(\cot^{2}{\left(5 x \right)} + 1\right)^{3} \log{\left(2 x \right)}}{\cot^{3}{\left(5 x \right)}} + \frac{500 \left(\cot^{2}{\left(5 x \right)} + 1\right)^{2} \log{\left(2 x \right)}}{\cot{\left(5 x \right)}} - 500 \left(\cot^{2}{\left(5 x \right)} + 1\right) \log{\left(2 x \right)} \cot{\left(5 x \right)} - \frac{75 \left(\cot^{2}{\left(5 x \right)} + 1\right)^{2}}{x \cot^{2}{\left(5 x \right)}} + \frac{150 \left(\cot^{2}{\left(5 x \right)} + 1\right)}{x} + \frac{15 \left(\cot^{2}{\left(5 x \right)} + 1\right)}{x^{2} \cot{\left(5 x \right)}} + \frac{2 \log{\left(\cot{\left(5 x \right)} \right)}}{x^{3}}\right) \cot^{\log{\left(2 x \right)}}{\left(5 x \right)}$$